CEGEP Calculus (Calcul Différentiel): Complete Study Guide

CEGEP Mathematics Overview

CEGEP (Collège d'enseignement général et professionnel) is the unique Quebec post-secondary system that bridges high school and university. Most students in Quebec complete 2 years of CEGEP before entering a 3-year university programme.

Mathematics at CEGEP is divided into three core calculus courses, taken sequentially as part of the pre-university science track (Sciences de la nature). These courses are recognised for credit at Quebec universities (McGill, Université de Montréal, Concordia, UQAM, and others).

The Three-Course Sequence

Students in computer science, engineering, or mathematics programmes typically take all three courses. For health sciences (nursing, pharmacy, physiotherapy pre-requisites), one calculus course may be sufficient depending on the programme.

Calculus 1 (201-NYA): Key Topics

Calcul Différentiel is the entry point and the course that students most frequently struggle with. It introduces rigorous mathematical analysis for the first time.

1. Limits and Continuity

• Definition of a limit (intuitive and formal)
• One-sided limits, infinite limits, limits at infinity
• Limit laws and algebraic techniques (factoring, rationalization, L'Hôpital's rule)
• Continuity: definition, types of discontinuity, Intermediate Value Theorem

2. Derivatives

• Definition of the derivative (limit of a difference quotient)
• Differentiation rules: power, product, quotient, chain rules
• Derivatives of trigonometric, exponential, and logarithmic functions
• Implicit differentiation
• Higher-order derivatives

3. Applications of Derivatives

• Critical points, increasing/decreasing intervals
• First and second derivative tests (local maxima/minima)
• Concavity and inflection points
• Curve sketching (combining all derivative information)
• Optimization problems (finding absolute maxima/minima)
• Related rates
• Mean Value Theorem (MVT)

Calculus 2 (201-NYB) Preview

Calcul Intégral builds directly on Calculus 1. You will encounter:

• Antiderivatives and indefinite integrals
• Definite integrals and the Fundamental Theorem of Calculus
• Integration techniques: substitution, integration by parts, partial fractions
• Applications: area between curves, volumes of revolution, arc length
• Improper integrals and sequences/series (at some CEGEPs)

Students who develop strong algebraic manipulation in Calculus 1 — especially factoring, trigonometric identities, and logarithm rules — find Calculus 2 significantly more manageable.

Study Tips

• Don't fall behind early. CEGEP Calculus moves fast — one week of missed content compounds significantly. Limits in week 2 are foundational for everything that follows.
• Practice without a calculator. While CEGEP exams sometimes permit calculators, the most important skill is algebraic manipulation by hand. Many professors design questions specifically to test this.
• Work through problems, not just examples. Reading a worked example creates the illusion of understanding. Only doing problems yourself builds genuine skill.
• Use the textbook systematically. The Calculus sequences at most Quebec CEGEPs use Stewart's Calculus (or equivalent). Work through the exercises at the end of each section — do not just read.
• Form a study group. Explaining problems to others is one of the most effective learning techniques, especially for application problems and curve sketching.

University Transition

CEGEP calculus is designed to prepare you for university-level analysis. Students entering McGill, Concordia, or UdeM in mathematics or engineering will encounter courses that assume fluency with all three CEGEP calculus courses.

• McGill's MATH 222 (Calculus 3) assumes both 201-NYA and 201-NYB are complete
• Engineering at Polytechnique Montréal requires all three courses as prerequisites
• For students from outside Quebec entering McGill, Concordia, etc.: AP Calculus AB is roughly equivalent to 201-NYA, and AP Calculus BC covers most of 201-NYB

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